Pine wood

We cut a carved beam from a pine trunk 6 m long and 35 cm in diameter. The beam's cross-section is in the shape of a square, which has the greatest area. Calculate the length of the sides of a square. Calculate the volume of lumber in cubic meters.

Correct answer:

a =  24.75 cm
V =  0.3675 m³

Step-by-step explanation:

$$\begin{gathered} D=35\text{cm} \\ L=6\text{m} \\ D=\sqrt{2}\cdot a \\ a=D/\sqrt{2}=35/\sqrt{2}=24.75\text{cm} \end{gathered}$$

$$\begin{gathered} A=a\to \text{m}=a:100\text{m}=24.7487:100\text{m}=0.24749\text{m} \\ V=A^2\cdot L=0.2475^2\cdot 6=0.3675{\text{m}}^3 \end{gathered}$$

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